Global monopoles in the extended Gauss-Bonnet gravity

Abstract

We discuss self-gravitating global O(3) monopole solutions associated with the spontaneous breaking of O(3) down to a global O(2) in an extended Gauss-Bonnet theory of gravity in ($3+1$) dimensions, in the presence of a nontrivial scalar field $\mathrm{\ensuremath{\Phi}}$ that couples to the Gauss-Bonnet higher curvature combination with a coupling parameter $\ensuremath{\alpha}$. We obtain a range of values for $\ensuremath{\alpha}<0$ (in our notation and conventions), which are such that a global (Israel type) matching is possible of the space-time exterior to the monopole core $\ensuremath{\delta}$ with a de Sitter interior, guaranteeing the positivity of the Arnowitt-Deser-Misner (ADM) mass of the monopole, which, together with a positive core radius $\ensuremath{\delta}>0$, are both dynamically determined as a result of this matching. It should be stressed that in the general relativity (GR) limit, where $\ensuremath{\alpha}\ensuremath{\rightarrow}0$, and $\mathrm{\ensuremath{\Phi}}\ensuremath{\rightarrow}\text{constant}$, such a matching yields a negative ADM monopole mass, which might be related to the stability issues the [Barriola-Vilenkin (BV)] global monopole of GR faces. Thus, our global monopole solution, which shares many features with the BV monopole, such as an asymptotic-space-time deficit angle, of potential phenomenological/cosmological interest, but has, par contrast, a positive ADM mass, has a chance of being a stable configuration, although a detailed stability analysis is pending.